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Computational Pharmacology

HDF applies methods of computational chemistry and physics to the solution of problems inherent to molecular biology and pharmacology. One member of the team has had 50 years experience using these methods to better understand anticonvulsant drug QSAR; beginning with relative primitive semi-empirical approximations, and eventually adopting ab initio (derived from theoretical principles) and DFT (density functional theory) methods to better understand mechanisms. Over twenty years ago he characterized the importance of cation (Ca⁺⁺)-π electron interactions that determine energies and conformations of certain antiepileptic drugs; using Amsterdam DFT.


Current work employs molecular mechanics (MM) and molecular dynamics (MD) in the study of protein structure (specifically Aβ) and Aβ folding. Other work invokes the more rigorous quantum mechanics (QM) methodology but only to the extent that we wish to study the interaction of a protein with a small molecule  where there might be orbital overlap or electronic bond formation. Using the MM/MD/QM methods we believe that we better understand the mechanism by which a few of our library compounds facilitate the action of endogenous brain protease action on SOAβ.


MM: Molecular Mechanics is a method which applies principles of classical Newtonian physics to determine the approximate position of an atom and its relationship to other atoms in a molecule. Electron correlation is ignored as the time required to determine protein structure would be too expensive. Computations employ a variety of so-called “force fields,” which may be determined either by experiment or by the application of ab initio methods. (A force field is simply a set of numbers or equations that are used to describe an energy landscape.)  The object of MM is typically to find the lowest (potential) energy molecular conformation.


MD: MM and MD are each based in classical Newtonian physics, and thus are similar. However, the principal use of MD is to model a trajectory of molecular motion, typically with the goal to achieve energy minimization.  Similar force fields are used as for MM. Combined MM/MD can provide important dynamic information, such as energy barriers between different conformers or steepness of a potential energy surface around a local minimum.


MM/MD/QM: Neither MM nor MD are adequate for the characterization of “chemistry” as such; meaning it provides no information concerning bond formation, mainly because electron correlation is neglected and differential overlap of atomic orbitals is not included. Yet it would be of intense interest if one could compute the chemical nature of a small molecule where it might interact with its protein receptor.  We are aware of the diverse nature of such interactions, most prominently hydrogen bonding; but also π-electron overlap, dipole and hydrophobic bonding, and the occasional covalent bond. Most macromolecules are typically impossible to model on most computers, using QM because the methodology is much more sophisticated than either MM or MD, and one might wait months or years to complete a computation, only to find it does not yield useful information.  


It is for this reason that we use a combination of MM and QM. MM often yields adequate information regarding secondary structure of a protein. Software exists that make it possible for a small molecule to find a “pocket” in a macromolecule where it might bind (“dock”), typically by non-covalent means. But such modeling is usually based on the size of the small molecule and the size of the pocket.  In this way potential receptor sites might be probed, and so-called pharmacophores discovered. However, the chemical nature of the interaction can not be explored without a higher level of computational power. 


Hence, the MM/QM ‘compromise.’  Given computer visualization of a putative pharmacophore in its putative receptor we can now zero in on that small segment of the protein that is involved in binding (by discarding the bulk of the protein not in proximity to the binding site).  It then  becomes reasonable in a computational sense to study the chemistry of the interaction, by methods described below. 


QM: There are many QM methods by which one might study the electronic structure of the interaction of a ligand with its receptor. Now that the protein/macromolecule has been “cut down to size” real possibilities exist. Most QM methods rely upon the so-called ‘linear combination of atomic orbitals’ (LCAO) as a way to approximate molecular orbitals. The rigorous ab initio methods, such as Hartree-Fock are an attempt to solve the Schrodinger equation, and in doing so obtain information such as orbital energies, charge densities, dipole moments and other electronic properties. DFT is becoming increasingly popular for larger systems mainly because it is faster than the true ab initio methods, yet gives useful results. Here the total energy is expressed as the sum of one-electron densities rather than the wave function, and is thus not a true attempt to approach the Schrodinger solution. These methods try to consider electron-electron repulsion (at least an average) and are thought of as “all-electron” or “many-electron” methods.  


Because early in the historical development of QM’s computational power was inadequate for Hartree-Fock or DFT solutions for very large molecules efforts were made to simplify the approximation of the Schrodinger equation (which can really only be solved exactly for very small systems).  Hence, the development of the so-called semi-empirical methods.  These methods include only the valence electrons and avoid differential overlap of orbitals to varying degrees in order to avoid electron repulsion integrals.  Hence, the abbreviation of methods such as CNDO (complete neglect of differential overlap), INDO (intermediate NDO), MNDO (modified NDO), etc.  While these studies have given a glimpse of what might approximate pharmacological reality, they are not satisfactory for most applications.


As such, most computational efforts involving large systems will utilize ab initio or DFT methods, considering that in the majority of studies the entire macromolecule will not of necessity be calculated.  On the other hand progress has been made in the “all-electron” study of entire enzyme systems using ab initio (e.g., Hartree-Fock) and techniques referred to as FMO, or fragment molecular orbital.

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